A reorganization, often shortened to reorg, occurs when a block is removed from the blockchain because a longer chain has been created. This is a damaging event to the Bitcoin network and especially to the miner(s) who mined the removed block(s) as they lose the block reward from that block. A reorganization occurs because Bitcoin nodes always accept the blockchain with the most blocks as the valid chain.
Imagine the blockchain is currently at block height 500. There are 500 blocks in the chain. One miner creates Block #501—we will call it 501a—and submits it to the network. Later, a different miner, who either missed Block #501a or maliciously ignores it, mines a different Block #501—we will call it 501b. Both blocks cannot be Block #501, so there are now two competing chains. Miners can choose which block they will mine on top of, and if miners add a new block on top of 501b, that chain is now longer than the 501a chain. All nodes will discard Block #501a, now called an orphan block, and adopt Block #501b and #502b as the valid chain.
This process does not only occur with single blocks. If conditions permit, any number of blocks can be reorganized out of the blockchain. If there are 510 blocks in a blockchain, and a miner decides to mine a different Block #500 and manages to create another 11 blocks, this new chain of 511 blocks will usurp the original chain.
However, while this malicious miner is mining these 12 blocks, honest miners will be mining on top of the original chain. By the time the malicious miner creates the new Block #500, the original chain could have 511 blocks or more. Thus, as outlined in the Bitcoin Whitepaper, the only way to ensure a successful reorganization is to have a majority of miners mining on the replacement chain, thus allowing the replacement chain to grow faster than the original chain. This is why mining decentralization and high hash rate are critical to Bitcoin’s security model. The higher and more decentralized the hashrate, the harder it is for a malicious miner to execute a reorganization.